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Statistical interaction potentially arises when there are two or more independent variables.  The effect of one independent variable may depend on the level of the other independent variable.  In order to find interaction, a factorial design is needed, in which the two independent variables are crossed with one another so that there are observations at every combination of levels of the two independent variables (Home).

An example is; In a study to check and see how taking coffee and energy drinks could lead to higher test scores. The independent variables are coffee and energy drinks, and the dependent variable is the test scores of the individuals.  The interaction would be the use of coffee and energy drinks together. On one hand using both could be harmful to the individual and result in them getting sick and lower test scores. While on the other hand they could have a great amount of sugar and caffeine in their system and be able to stay awake and study longer, resulting in higher test scores. Using a factorial design we can compare the use of coffee and energy drinks together on test scores, the effect of only coffee on test scores and the effect of only energy drinks on test scores. 

Home. (n.d.). Finding Interactions [Digital image]. Retrieved April 4, 2017, from https://courses.washington.edu/smartpsy/interactions.htm